Distance vs. time. Acoustic and articulatory consequences of reduced vowel duration in Polish*

1 Overview

This supplementary document complements the paper Distance vs. time. Articulatory and acoustic consequences of reduced vowel duration in Polish.

The following sections illustrate:

The data extracted from ultrasound images, and the formants.
Descriptive plots of the raw data.
Code and plots of the linear regression models.
Summaries of the models in 3.
Extra analyses of F0.

Only relevant R code is shown in this document. The full code can be inspected on the OSF repository at https://osf.io/hy7nt/?view_only=d06775a2cb1d4786a0442b0f15d73296, in the file code/analysis.Rmd.

2 Atriculatory data processing

This is Figure 1 from the paper, which illustrates the articulatory data processing, as well as vowel formants. See paper for details.

3 Descriptive statistics plots

3.1 Articulatory undershoot

Tongue contours from ultrasound tongue imaging of speaker PL01. Tongue tip on the right.

3.2 Duration

Figure 2 from the paper with boxplots and means of vowel duration depending on speech rate and stress.

3.3 Vowel spaces

4 Inferential statistics

4.1 VIF (multicollinearity)

VIF values below 3 indicate absence of multicollinearity (Zuur, Ieno, and Elphick 2010). For all predictors, VIF < 3.

Variables	VIF
duration	2.169934
f1.z	1.379401
f2.z	1.208097
f0.z	1.122029
rate	1.639475
stress	1.451903

4.2 Duration

	npar	AIC	BIC	logLik	deviance	Chisq	Df	Pr(>Chisq)
dur.lmer3	31	-291.7616	-128.3173	176.8808	-353.7616	NA	NA	NA
dur.lmer2	33	-341.1601	-167.1710	203.5801	-407.1601	53.39852	2	0
dur.lmer.full	48	-375.6100	-122.5349	235.8050	-471.6100	64.44983	15	0

4.3 F1

	npar	AIC	BIC	logLik	deviance	Chisq	Df	Pr(>Chisq)
f1.lmer.base	15	1760.472	1839.558	-865.2361	1730.472	NA	NA	NA
f1.lmer.stress1	16	1697.351	1781.709	-832.6755	1665.351	65.12115	1	0e+00
f1.lmer.stress2	21	1671.028	1781.748	-814.5139	1629.028	36.32313	5	8e-07

## # R2 for Mixed Models
## 
##   Conditional R2: 0.830
##      Marginal R2: 0.772

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.828

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.832

## V1 = a:
##  contrast              estimate     SE   df t.ratio p.value
##  unstressed - stressed  -0.1947 0.0803 70.9 -2.426  0.0178 
## 
## V1 = e:
##  contrast              estimate     SE   df t.ratio p.value
##  unstressed - stressed  -0.3938 0.0721 46.9 -5.462  <.0001 
## 
## V1 = i:
##  contrast              estimate     SE   df t.ratio p.value
##  unstressed - stressed  -0.0232 0.0708 43.8 -0.328  0.7444 
## 
## V1 = o:
##  contrast              estimate     SE   df t.ratio p.value
##  unstressed - stressed  -0.4242 0.0750 54.8 -5.655  <.0001 
## 
## V1 = u:
##  contrast              estimate     SE   df t.ratio p.value
##  unstressed - stressed  -0.0926 0.0759 57.4 -1.219  0.2277 
## 
## V1 = ɨ:
##  contrast              estimate     SE   df t.ratio p.value
##  unstressed - stressed  -0.1340 0.0739 51.7 -1.813  0.0756 
## 
## Degrees-of-freedom method: kenward-roger

V1	duration.trend	SE	df	t.ratio	p.value
a	0.0188220	0.0012463	1387.754	15.1027779	0.0000000
e	0.0089742	0.0013664	1410.827	6.5679103	0.0000000
i	-0.0034263	0.0013199	1385.225	-2.5959280	0.0095333
o	0.0027981	0.0011339	1408.425	2.4675926	0.0137207
u	0.0012137	0.0013415	1398.657	0.9047526	0.3657523
ɨ	0.0009668	0.0010876	1406.486	0.8889355	0.3741898

4.4 F2

	npar	AIC	BIC	logLik	deviance	Chisq	Df	Pr(>Chisq)
f2.lmer.base	15	686.0166	765.1026	-328.0083	656.0166	NA	NA	NA
f2.lmer.stress1	16	685.7771	770.1354	-326.8885	653.7771	2.239533	1	0.1345216
f2.lmer.stress2	21	660.6134	771.3337	-309.3067	618.6134	35.163703	5	0.0000014

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.906

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.907

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.909

V1	duration.trend	SE	df	t.ratio	p.value
a	0.0010623	0.0007896	71.72053	1.345283	0.1827721
e	0.0036083	0.0009683	153.87450	3.726346	0.0002723
i	0.0064001	0.0009630	149.92347	6.645943	0.0000000
o	-0.0046407	0.0007924	72.27819	-5.856616	0.0000001
u	-0.0061957	0.0008945	114.65049	-6.926301	0.0000000
ɨ	0.0035699	0.0007826	67.64431	4.561831	0.0000219

4.5 Z1

	npar	AIC	BIC	logLik	deviance	Chisq	Df	Pr(>Chisq)
z1.lmer.base	15	1079.825	1158.911	-524.9127	1049.825	NA	NA	NA
z1.lmer.stress1	16	1078.523	1162.882	-523.2617	1046.523	3.301855	1	0.0692017
z1.lmer.stress2	21	1080.686	1191.407	-519.3431	1038.686	7.837281	5	0.1654343

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.731

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.732

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.732

V1	duration.trend	SE	df	t.ratio	p.value
a	0.0088917	0.0011077	27.49535	8.0269993	0.0000000
e	0.0041344	0.0012787	48.22526	3.2334337	0.0022094
i	-0.0009243	0.0012737	47.31917	-0.7256695	0.4716154
o	0.0094759	0.0011100	27.75403	8.5371785	0.0000000
u	0.0000687	0.0012072	38.57507	0.0569243	0.9548993
ɨ	-0.0004451	0.0011012	26.79854	-0.4042152	0.6892624

4.6 Z2

	npar	AIC	BIC	logLik	deviance	Chisq	Df	Pr(>Chisq)
z2.lmer.base	15	753.9717	833.0577	-361.9858	723.9717	NA	NA	NA
z2.lmer.stress1	16	755.9562	840.3146	-361.9781	723.9562	0.0154439	1	0.9010988
z2.lmer.stress2	21	760.4627	871.1831	-359.2314	718.4627	5.4935092	5	0.3586581

## # R2 for Mixed Models
## 
##   Conditional R2: 0.896
##      Marginal R2: 0.721

## # R2 for Mixed Models
## 
##   Conditional R2: 0.895
##      Marginal R2: 0.721

## # R2 for Mixed Models
## 
##   Conditional R2: 0.896
##      Marginal R2: 0.721

V1	duration.trend	SE	df	t.ratio	p.value
a	-0.0031410	0.0009973	25.64689	-3.1493657	0.0041252
e	-0.0006506	0.0011446	44.07179	-0.5684129	0.5726397
i	0.0040653	0.0011405	43.36942	3.5644529	0.0009023
o	-0.0066949	0.0009992	25.86902	-6.7001979	0.0000004
u	-0.0035357	0.0010826	35.41626	-3.2660975	0.0024243
ɨ	0.0035870	0.0009917	25.02169	3.6172118	0.0013131

5 Model summaries

5.1 Duration

	duration.log
Predictors	Estimates	CI	p	df
(Intercept)	4.3187	4.1263 – 4.5111	<0.001	14.8100
rate [normal]	-0.2209	-0.3372 – -0.1046	0.00041	43.2044
rate [fast]	-0.4046	-0.5810 – -0.2281	0.00016	16.4521
V1 [e]	-0.1048	-0.3544 – 0.1449	0.37010	9.6185
V1 [i]	-0.1178	-0.3944 – 0.1588	0.35959	8.8555
V1 [o]	-0.0733	-0.1675 – 0.0208	0.12679	1367.8525
V1 [u]	-0.3184	-0.5950 – -0.0418	0.02863	8.8555
V1 [ɨ]	0.0229	-0.2537 – 0.2995	0.85529	8.8555
stress [stressed]	0.4710	0.3768 – 0.5652	<0.001	238.9499
rate [normal] * V1 [e]	-0.0473	-0.1707 – 0.0761	0.45222	1361.0048
rate [fast] * V1 [e]	-0.0470	-0.1705 – 0.0764	0.45501	1361.0048
rate [normal] * V1 [i]	0.0429	-0.0805 – 0.1663	0.49544	1361.0048
rate [fast] * V1 [i]	-0.0223	-0.1457 – 0.1011	0.72313	1361.0048
rate [normal] * V1 [o]	-0.0607	-0.1842 – 0.0627	0.33475	1361.0048
rate [fast] * V1 [o]	-0.0667	-0.1901 – 0.0567	0.28941	1361.0048
rate [normal] * V1 [u]	-0.0806	-0.2040 – 0.0429	0.20060	1361.0048
rate [fast] * V1 [u]	-0.0502	-0.1736 – 0.0733	0.42553	1361.0048
rate [normal] * V1 [ɨ]	-0.0581	-0.1815 – 0.0653	0.35608	1361.0048
rate [fast] * V1 [ɨ]	-0.0838	-0.2073 – 0.0396	0.18305	1361.0048
rate [normal] * stress [stressed]	-0.0019	-0.1253 – 0.1215	0.97590	1361.0048
rate [fast] * stress [stressed]	-0.1241	-0.2475 – -0.0007	0.04880	1361.0048
V1 [e] * stress [stressed]	-0.1580	-0.2815 – -0.0346	0.01213	1361.0048
V1 [i] * stress [stressed]	-0.2180	-0.3415 – -0.0946	0.00055	1361.0048
V1 [o] * stress [stressed]	-0.0017	-0.1252 – 0.1217	0.97795	1361.0048
V1 [u] * stress [stressed]	0.0419	-0.0816 – 0.1653	0.50578	1361.0048
V1 [ɨ] * stress [stressed]	-0.0527	-0.1761 – 0.0707	0.40247	1361.0048
(rate [normal] * V1 [e]) * stress [stressed]	-0.0292	-0.2037 – 0.1454	0.74299	1361.0048
(rate [fast] * V1 [e]) * stress [stressed]	-0.0129	-0.1875 – 0.1617	0.88478	1361.0048
(rate [normal] * V1 [i]) * stress [stressed]	-0.0241	-0.1987 – 0.1505	0.78666	1361.0048
(rate [fast] * V1 [i]) * stress [stressed]	0.0225	-0.1521 – 0.1970	0.80075	1361.0048
(rate [normal] * V1 [o]) * stress [stressed]	-0.0624	-0.2369 – 0.1122	0.48338	1361.0048
(rate [fast] * V1 [o]) * stress [stressed]	-0.0897	-0.2643 – 0.0848	0.31347	1361.0048
(rate [normal] * V1 [u]) * stress [stressed]	-0.0273	-0.2018 – 0.1473	0.75924	1361.0048
(rate [fast] * V1 [u]) * stress [stressed]	-0.1707	-0.3452 – 0.0039	0.05532	1361.0048
(rate [normal] * V1 [ɨ]) * stress [stressed]	-0.0381	-0.2127 – 0.1365	0.66853	1361.0048
(rate [fast] * V1 [ɨ]) * stress [stressed]	-0.0843	-0.2589 – 0.0903	0.34366	1361.0048
Random Effects
σ²	0.0396
τ₀₀ _frame	0.0154
τ₀₀ _speaker	0.0193
τ₁₁ _{speaker.ratenormal}	0.0135
τ₁₁ _{speaker.ratefast}	0.0498
τ₁₁ _{speaker.stressstressed}	0.0031
ρ₀₁ _{speaker.ratenormal}	-0.6410
ρ₀₁ _{speaker.ratefast}	-0.5484
ρ₀₁ _{speaker.stressstressed}	-0.9139
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.706 / NA

5.2 F1

	f1.z
Predictors	Estimates	CI	p	df
(Intercept)	0.1655	-0.2195 – 0.5504	0.36633	11.6159
V1 [e]	-0.8117	-1.3554 – -0.2681	0.00709	11.4664
V1 [i]	-0.9752	-1.5739 – -0.3766	0.00452	10.2636
V1 [o]	-0.3559	-0.5738 – -0.1381	0.00138	1405.5179
V1 [u]	-0.9014	-1.4958 – -0.3071	0.00717	9.6528
V1 [ɨ]	-0.7690	-1.3653 – -0.1726	0.01660	9.9580
duration	0.0188	0.0164 – 0.0213	<0.001	1387.7540
stress [stressed]	0.1947	0.0346 – 0.3547	0.01783	70.9286
V1 [e] * duration	-0.0098	-0.0135 – -0.0062	<0.001	1412.7627
V1 [i] * duration	-0.0222	-0.0258 – -0.0187	<0.001	1413.7521
V1 [o] * duration	-0.0160	-0.0193 – -0.0127	<0.001	1410.9211
V1 [u] * duration	-0.0176	-0.0212 – -0.0140	<0.001	1411.8737
V1 [ɨ] * duration	-0.0179	-0.0211 – -0.0146	<0.001	1409.6337
V1 [e] * stress [stressed]	0.1991	0.0228 – 0.3753	0.02687	1404.6665
V1 [i] * stress [stressed]	-0.1714	-0.3457 – 0.0029	0.05387	1404.0928
V1 [o] * stress [stressed]	0.2295	0.0487 – 0.4104	0.01288	1403.3462
V1 [u] * stress [stressed]	-0.1021	-0.2845 – 0.0803	0.27231	1404.7296
V1 [ɨ] * stress [stressed]	-0.0607	-0.2398 – 0.1183	0.50609	1402.6657
Random Effects
σ²	0.1740
τ₀₀ _frame	0.0697
τ₀₀ _speaker	0.0029
τ₁₁ _{speaker.stressstressed}	0.0178
ρ₀₁ _speaker	-1.0000
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.836 / NA

5.3 F2

	f2.z
Predictors	Estimates	CI	p	df
(Intercept)	-0.3897	-0.7957 – 0.0163	0.05794	8.8492
V1 [e]	0.6104	0.0373 – 1.1836	0.03937	8.7240
V1 [i]	1.6015	0.9638 – 2.2391	0.00038	8.2679
V1 [o]	-0.2358	-0.3885 – -0.0831	0.00249	1411.1814
V1 [u]	-0.3495	-0.9855 – 0.2866	0.24094	8.0210
V1 [ɨ]	0.4526	-0.1841 – 1.0894	0.14020	8.1408
duration	0.0011	-0.0005 – 0.0026	0.18277	71.7205
V1 [e] * duration	0.0025	0.0003 – 0.0048	0.02587	1419.9932
V1 [i] * duration	0.0053	0.0031 – 0.0076	<0.001	1419.3853
V1 [o] * duration	-0.0057	-0.0076 – -0.0038	<0.001	1412.3655
V1 [u] * duration	-0.0073	-0.0094 – -0.0051	<0.001	1417.6616
V1 [ɨ] * duration	0.0025	0.0006 – 0.0044	0.01082	1412.6052
Random Effects
σ²	0.0889
τ₀₀ _frame	0.0842
τ₀₀ _speaker	0.0043
τ₁₁ _{speaker.duration}	0.0000
ρ₀₁ _speaker	-1.0000
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.907 / NA

5.4 Z1

	z1
Predictors	Estimates	CI	p	df
(Intercept)	-0.0013	-0.2825 – 0.2799	0.99230	16.5061
V1 [e]	-0.4182	-0.7976 – -0.0389	0.03314	13.3278
V1 [i]	-0.8547	-1.2696 – -0.4398	0.00078	11.5918
V1 [o]	-0.0092	-0.1832 – 0.1648	0.91747	1411.4250
V1 [u]	-0.0972	-0.5074 – 0.3130	0.61118	10.6587
V1 [ɨ]	-0.0935	-0.5058 – 0.3188	0.62769	11.1077
duration	0.0089	0.0066 – 0.0112	<0.001	27.4954
V1 [e] * duration	-0.0048	-0.0073 – -0.0022	0.00026	1418.6184
V1 [i] * duration	-0.0098	-0.0124 – -0.0073	<0.001	1419.1450
V1 [o] * duration	0.0006	-0.0016 – 0.0028	0.60526	1413.4468
V1 [u] * duration	-0.0088	-0.0112 – -0.0064	<0.001	1415.6416
V1 [ɨ] * duration	-0.0093	-0.0115 – -0.0071	<0.001	1412.0221
Random Effects
σ²	0.1154
τ₀₀ _frame	0.0320
τ₀₀ _speaker	0.0239
τ₁₁ _{speaker.duration}	0.0000
ρ₀₁ _speaker	-0.9948
ICC	0.2402
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.680 / 0.757

5.5 Z2

	z2
Predictors	Estimates	CI	p	df
(Intercept)	-0.1205	-0.6668 – 0.4257	0.62680	8.4109
V1 [e]	0.5192	-0.2493 – 1.2877	0.15759	7.9250
V1 [i]	1.2666	0.4094 – 2.1238	0.00950	7.6823
V1 [o]	-0.2783	-0.4311 – -0.1255	0.00036	1408.2080
V1 [u]	-0.5101	-1.3663 – 0.3462	0.20469	7.5513
V1 [ɨ]	0.1881	-0.6686 – 1.0448	0.62395	7.6137
duration	-0.0031	-0.0052 – -0.0011	0.00413	25.6469
V1 [e] * duration	0.0025	0.0002 – 0.0047	0.02945	1412.6676
V1 [i] * duration	0.0072	0.0050 – 0.0094	<0.001	1412.9083
V1 [o] * duration	-0.0036	-0.0055 – -0.0016	0.00035	1408.6364
V1 [u] * duration	-0.0004	-0.0025 – 0.0017	0.71441	1412.3145
V1 [ɨ] * duration	0.0067	0.0048 – 0.0087	<0.001	1408.1702
Random Effects
σ²	0.0889
τ₀₀ _frame	0.1548
τ₀₀ _speaker	0.0190
τ₁₁ _{speaker.duration}	0.0000
ρ₀₁ _speaker	-0.9900
ICC	0.6412
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.722 / 0.900

6 Further exploratory analyses

6.1 F0

	npar	AIC	BIC	logLik	deviance	Chisq	Df	Pr(>Chisq)
f0.lmer1	11	3832.230	3890.196	-1905.115	3810.230	NA	NA	NA
f0.lmer2	16	3816.583	3900.897	-1892.292	3784.583	25.6465446	5	0.0001045
f0.lmer3	21	3825.897	3936.559	-1891.948	3783.897	0.6864549	5	0.9837038

	f0.z
Predictors	Estimates	CI	p
(Intercept)	-0.65	-0.82 – -0.49	<0.001
V11	0.11	-0.23 – 0.46	0.520
V12	0.09	-0.28 – 0.46	0.629
V13	-0.26	-0.64 – 0.11	0.171
V14	0.04	-0.28 – 0.36	0.820
V15	0.39	0.05 – 0.74	0.026
duration	0.01	0.01 – 0.01	<0.001
stress [stressed]	0.29	0.19 – 0.40	<0.001
V11 * duration	-0.01	-0.01 – -0.00	0.001
V12 * duration	-0.00	-0.01 – 0.00	0.055
V13 * duration	0.00	-0.00 – 0.01	0.053
V14 * duration	-0.00	-0.01 – 0.00	0.187
V15 * duration	0.01	0.00 – 0.01	0.018
Random Effects
σ²	0.81
τ₀₀ _frame	0.03
τ₀₀ _speaker	0.00
N _speaker	10
N _frame	12
Observations	1436
Marginal R² / Conditional R²	0.186 / NA

7 Session info

## ─ Session info ───────────────────────────────────────────────────────────────
##  setting  value                       
##  version  R version 4.0.3 (2020-10-10)
##  os       macOS Big Sur 10.16         
##  system   x86_64, darwin17.0          
##  ui       X11                         
##  language (EN)                        
##  collate  en_US.UTF-8                 
##  ctype    en_US.UTF-8                 
##  tz       Europe/Berlin               
##  date     2021-04-07                  
## 
## ─ Packages ───────────────────────────────────────────────────────────────────
##  ! package      * version    date       lib
##  P abind          1.4-5      2016-07-21 [?]
##  P assertthat     0.2.1      2019-03-21 [?]
##  P backports      1.2.1      2020-12-09 [?]
##  P bayestestR     0.8.2      2021-01-26 [?]
##  P bookdown       0.21       2020-10-13 [?]
##  P boot           1.3-27     2021-02-12 [4]
##  P broom          0.7.5      2021-02-19 [?]
##  P cachem         1.0.4      2021-02-13 [?]
##  P callr          3.5.1      2020-10-13 [?]
##  P car            3.0-10     2020-09-29 [?]
##  P carData      * 3.0-4      2020-05-22 [?]
##  P cellranger     1.1.0      2016-07-27 [?]
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##  P codetools      0.2-18     2020-11-04 [4]
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##  P dbplyr         2.1.0      2021-02-03 [?]
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##  P ggrepel      * 0.9.1      2021-01-15 [?]
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##  P readr        * 1.4.0      2020-10-05 [?]
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##  P sp           * 1.4-5      2021-01-10 [?]
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##  P stringr      * 1.4.0      2019-02-10 [?]
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##  P tidyselect     1.1.0      2020-05-11 [?]
##  P tidyverse    * 1.3.0      2019-11-21 [?]
##  P usdm         * 1.1-18     2017-06-25 [?]
##  P usethis        2.0.1      2021-02-10 [?]
##  P utf8           1.2.1      2021-03-12 [?]
##  P vctrs          0.3.6      2020-12-17 [?]
##  P withr          2.4.1      2021-01-26 [?]
##  P xfun           0.22       2021-03-11 [?]
##  P xml2           1.3.2      2020-04-23 [?]
##  P xtable         1.8-4      2019-04-21 [?]
##  P yaml           2.2.1      2020-02-01 [?]
##  P zip            2.1.1      2020-08-27 [?]
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## 
## [1] /Users/ste/repos/polish-reduction/renv/library/R-4.0/x86_64-apple-darwin17.0
## [2] /private/var/folders/yj/b5zvw9lj2zg6tp920wyg14y80000gn/T/RtmphaROrW/renv-system-library
## [3] /Library/Frameworks/R.framework/Versions/4.0/Resources/site-library
## [4] /Library/Frameworks/R.framework/Versions/4.0/Resources/library
## 
##  P ── Loaded and on-disk path mismatch.

Zuur, Alain F., Elena N. Ieno, and Chris S. Elphick. 2010. “A Protocol for Data Exploration to Avoid Common Statistical Problems.” Methods in Ecology and Evolution 1 (1): 3–14. https://doi.org/10.1111/j.2041-210X.2009.00001.x.